Gauss's theorem is one of the fundamental laws of electrodynamics, structurally included in the system of equations of another great scientist - Maxwell. It expresses the relationship between the intensity flows of both electrostatic and electrodynamic fields passing through a closed surface. The name of Karl Gauss sounds in the scientific world no less loudly than, for example, Archimedes, Newton or Lomonosov. In physics, astronomy and mathematics, there are not many areas that this brilliant German scientist did not directly contribute to the development of.
Gauss's theorem has played a key role in the study and understanding of the nature of electromagnetism. By and large, it has become a kind of generalization and, to some extent, an interpretation of the well-known Coulomb's law. This is just the case, not so rare in science, when the same phenomena can be described and formulated in different ways. But the Gauss theorem not only acquired appliedmeaning and practical application, it helped to look at the known laws of nature from a slightly different perspective.
In some ways, she contributed to a grand breakthrough in science, laying the foundation for modern knowledge in the field of electromagnetism. So what is the Gauss theorem and what is its practical application? If we take a pair of static point charges, then the particle brought to them will be attracted or repelled with a force that is equal to the algebraic sum of the values of all elements of the system. In this case, the intensity of the general aggregate field formed as a result of such an interaction will be the sum of its individual components. This relation has become widely known as the principle of superposition, which allows one to accurately describe any system created by multi-vector charges, regardless of their total number.
However, when there are a lot of such particles, scientists at first encountered certain difficulties in the calculations, which could not be resolved by applying Coulomb's law. The Gauss theorem for the magnetic field helped to overcome them, which, however, is valid for any force systems of charges that have a decreasing intensity proportional to r −2. Its essence boils down to the fact that an arbitrary number of charges surrounded by a closed surface will have a total intensity flux equal to the total value of the electric potential of each point of the given plane. At the same time, the principles of interaction between elements are not taken into account, which greatly simplifiescalculations. Thus, this theorem makes it possible to calculate the field even with an infinite number of electric charge carriers.
True, in reality this is feasible only in some cases of their symmetrical arrangement, when there is a convenient surface through which the strength and intensity of the flow can be easily calculated. For example, a test charge placed inside a conducting body of a spherical shape will not experience the slightest force effect, since the field strength index there is equal to zero. The ability of conductors to push out various electrical fields is due solely to the presence of charge carriers in them. In metals, this function is performed by electrons. Such features are widely used today in technology to create various spatial regions in which electric fields do not act. These phenomena are perfectly explained by the Gauss theorem for dielectrics, whose influence on systems of elementary particles is reduced to the polarization of their charges.
To create such effects, it is enough to surround a certain area of tension with a metal shielding mesh. This is how sensitive high-precision devices and people are protected from exposure to electric fields.
